This document summarizes Rick Gilmore’s analysis of the Jaccard index data.
The goal is to explore ways to generate an empirical “null” distribution of the Jaccard index data to compare it to the observed data.
Note: I have set eval=FALSE for a series of chunks below that generate the permuted sorting and Jaccard index data. These take many minutes to run.
/analysis/data/{P1,P31M,P3M1,P6,P6M}-sorting.csv and create new CSVs with the permuted values.analysis/make.jaccard.df.R function.n times, where n is large, probably 1,000.Let’s build and test a permutation function for the raw sorting data.
Now, let’s generate multiple permuted CSVs.
generate_n_sorting_permutations <-
function(wp_group = "P1",
n_permutations = 5) {
csv_in <- paste0("analysis/data/", wp_group, "-sorting.csv")
if (!file.exists(csv_in)) {
stop(paste0("`csv_in` not found: ", csv_in))
}
df_in <- readr::read_csv(csv_in)
df_exemplars <- df_in[, -c(1, 2, 23, 24)]
out_m <- as.matrix(df_exemplars)
for (p in 1:n_permutations) {
csv_out <-
paste0(
"analysis/data/permutation_analysis/sorting_csv/",
wp_group,
"-sorting-perm-",
stringr::str_pad(p, 3, pad = 0), ".csv"
)
for (r in 1:dim(out_m)[1]) {
new_i <- sample(1:20)
out_m[r, 1:20] <- out_m[r, new_i]
}
array_out <-
as.data.frame(cbind(df_in$Participant, df_in$Set, out_m, df_in$Set_size, df_in$Group))
# Rename!
names(array_out) <-
c("Participant",
"Set",
names(df_exemplars),
"Set_size",
"Group")
array_out
readr::write_csv(array_out, csv_out)
}
}
Then we test it.
generate_n_sorting_permutations()
##
## ── Column specification ────────────────────────────────────────────────────────
## cols(
## .default = col_double(),
## Participant = col_character(),
## Group = col_character()
## )
## ℹ Use `spec()` for the full column specifications.
Now, let’s confirm that we can calculate Jaccard indices from these data.
make_jaccard_csvs <- function(wallpaper_group = "P1",
duplicates = FALSE,
input_dir = 'analysis/data/permutation_analysis/sorting_csv/',
output_dir = 'analysis/data/permutation_analysis/jaccards/') {
# Makes a data.frame from the raw sorting data
# Load externals
source("analysis/jaccard.data.R")
source("analysis/jaccard.R")
these_csvs <-
list.files(input_dir, paste0("^", wallpaper_group, "\\-"), full.names = TRUE)
purrr::map(these_csvs,
calculate_save_jaccard_df,
wallpaper_group,
jaccard_dir = output_dir)
}
# Load a sorting permutation file, calculate the Jaccard indices, and (conditionally) save it to file.
calculate_save_jaccard_df <- function(this_csv,
wallpaper_group,
save_output = TRUE,
jaccard_dir = "analysis/data/permutation_analysis/jaccards/",
vb = FALSE) {
this_fn <- basename(this_csv)
this_perm_number <- stringr::str_extract(this_fn, "[0-9]{3}")
out_fn <-
paste0(jaccard_dir,
wallpaper_group,
"-jaccard-",
this_perm_number,
".csv")
this_df <- readr::read_csv(this_csv)
# Calculate Jaccard
jaccard_df <- jaccard.data(this_df)
if (save_output) {
if (vb) message(paste0('Saving ', out_fn))
readr::write_csv(jaccard_df, out_fn)
} else {
jaccard_df
}
}
make_jaccard_csvs()
generate_n_sorting_permutations("P1", n_permutations = 999)
make_jaccard_csvs("P1")
generate_n_sorting_permutations("P31M", n_permutations = 999)
make_jaccard_csvs("P31M")
generate_n_sorting_permutations("P3M1", n_permutations = 999)
make_jaccard_csvs("P3M1")
generate_n_sorting_permutations("P6", n_permutations = 999)
make_jaccard_csvs("P6")
generate_n_sorting_permutations("P6M", n_permutations = 999)
make_jaccard_csvs("P6M")
make_perm_jaccard_df <- function(this_csv) {
this_fn <- basename(this_csv)
this_perm_number <- stringr::str_extract(this_fn, "[0-9]{3}")
this_df <- readr::read_csv(this_csv)
this_df <- this_df %>%
dplyr::mutate(
.,
exemplar_pair = paste0(
stringr::str_extract(Exemplar.Row, "[0-9]{3}$"),
"-",
stringr::str_extract(Exemplar.Col, "[0-9]{3}$")
),
perm = this_perm_number
)
this_df
}
make_aggregate_perm_jaccard_df <- function(wp_group = "P1",
input_dir = "analysis/data/permutation_analysis/jaccards",
save_csv = TRUE,
output_dir = "analysis/data/permutation_analysis/aggregates",
vb = TRUE) {
these_csvs <-
list.files(input_dir, paste0("^", wp_group, "\\-"), full.names = TRUE)
df <- purrr::map_df(these_csvs, make_perm_jaccard_df)
if (save_csv) {
out_fn <- file.path(output_dir, paste0(wp_group, "-aggregate-perm-jaccard.csv"))
if (vb) message(paste0("Saving ", out_fn))
readr::write_csv(df, out_fn)
} else {
df
}
}
Import the data.
P1_perm_df <- make_aggregate_perm_jaccard_df("P1")
P1_perm_df <- readr::read_csv("analysis/data/permutation_analysis/aggregates/P1-aggregate-perm-jaccard.csv")
##
## ── Column specification ────────────────────────────────────────────────────────
## cols(
## Exemplar.Row = col_double(),
## Exemplar.Col = col_double(),
## Jaccard = col_double(),
## Group = col_character(),
## exemplar_pair = col_character(),
## perm = col_character()
## )
Visualize.
P1_perm_df %>%
ggplot2::ggplot(.) +
ggplot2::aes(x = Jaccard) +
ggplot2::geom_histogram(bins = 50)
Generate summary stats by exemplar pair.
P1_perm_stats_df <- P1_perm_df %>%
dplyr::group_by(., Group, exemplar_pair) %>%
dplyr::summarize(., jaccard_mean = mean(Jaccard),
jaccard_sd = sd(Jaccard))
## `summarise()` has grouped output by 'Group'. You can override using the `.groups` argument.
Import the data.
P31M_perm_df <- make_aggregate_perm_jaccard_df("P31M")
P31M_perm_df <- readr::read_csv("analysis/data/permutation_analysis/aggregates/P31M-aggregate-perm-jaccard.csv")
##
## ── Column specification ────────────────────────────────────────────────────────
## cols(
## Exemplar.Row = col_double(),
## Exemplar.Col = col_double(),
## Jaccard = col_double(),
## Group = col_character(),
## exemplar_pair = col_character(),
## perm = col_character()
## )
Visualize.
P31M_perm_df %>%
ggplot2::ggplot(.) +
ggplot2::aes(x = Jaccard) +
ggplot2::geom_histogram(bins = 50)
Generate summary stats by exemplar pair.
P31M_perm_stats_df <- P31M_perm_df %>%
dplyr::group_by(., Group, exemplar_pair) %>%
dplyr::summarize(., jaccard_mean = mean(Jaccard),
jaccard_sd = sd(Jaccard))
## `summarise()` has grouped output by 'Group'. You can override using the `.groups` argument.
Import the data.
P3M1_perm_df <- make_aggregate_perm_jaccard_df("P3M1")
P3M1_perm_df <- readr::read_csv("analysis/data/permutation_analysis/aggregates/P3M1-aggregate-perm-jaccard.csv")
##
## ── Column specification ────────────────────────────────────────────────────────
## cols(
## Exemplar.Row = col_double(),
## Exemplar.Col = col_double(),
## Jaccard = col_double(),
## Group = col_character(),
## exemplar_pair = col_character(),
## perm = col_character()
## )
Visualize.
P3M1_perm_df %>%
ggplot2::ggplot(.) +
ggplot2::aes(x = Jaccard) +
ggplot2::geom_histogram(bins = 50)
Generate summary stats by exemplar pair.
P3M1_perm_stats_df <- P3M1_perm_df %>%
dplyr::group_by(., Group, exemplar_pair) %>%
dplyr::summarize(., jaccard_mean = mean(Jaccard),
jaccard_sd = sd(Jaccard))
## `summarise()` has grouped output by 'Group'. You can override using the `.groups` argument.
Import the data.
P6_perm_df <- make_aggregate_perm_jaccard_df("P6")
P6_perm_df <- readr::read_csv("analysis/data/permutation_analysis/aggregates/P6-aggregate-perm-jaccard.csv")
##
## ── Column specification ────────────────────────────────────────────────────────
## cols(
## Exemplar.Row = col_double(),
## Exemplar.Col = col_double(),
## Jaccard = col_double(),
## Group = col_character(),
## exemplar_pair = col_character(),
## perm = col_character()
## )
Visualize.
P6_perm_df %>%
ggplot2::ggplot(.) +
ggplot2::aes(x = Jaccard) +
ggplot2::geom_histogram(bins = 50)
Generate summary stats by exemplar pair.
P6_perm_stats_df <- P6_perm_df %>%
dplyr::group_by(., Group, exemplar_pair) %>%
dplyr::summarize(., jaccard_mean = mean(Jaccard),
jaccard_sd = sd(Jaccard))
## `summarise()` has grouped output by 'Group'. You can override using the `.groups` argument.
Import the data.
P6M_perm_df <- make_aggregate_perm_jaccard_df("P6M")
P6M_perm_df <- readr::read_csv("analysis/data/permutation_analysis/aggregates/P6M-aggregate-perm-jaccard.csv")
##
## ── Column specification ────────────────────────────────────────────────────────
## cols(
## Exemplar.Row = col_double(),
## Exemplar.Col = col_double(),
## Jaccard = col_double(),
## Group = col_character(),
## exemplar_pair = col_character(),
## perm = col_character()
## )
Visualize.
P6M_perm_df %>%
ggplot2::ggplot(.) +
ggplot2::aes(x = Jaccard) +
ggplot2::geom_histogram(bins = 50)
Generate summary stats by exemplar pair.
P6M_perm_stats_df <- P6M_perm_df %>%
dplyr::group_by(., Group, exemplar_pair) %>%
dplyr::summarize(., jaccard_mean = mean(Jaccard),
jaccard_sd = sd(Jaccard))
## `summarise()` has grouped output by 'Group'. You can override using the `.groups` argument.
jaccard_perm_df <- rbind(P1_perm_df, P31M_perm_df, P3M1_perm_df, P6_perm_df, P6M_perm_df)
Visualization.
jaccard_perm_df %>%
ggplot(.) +
aes(Jaccard, color = Group) +
facet_grid(Group ~ .) +
geom_boxplot(bins = 50)
## Warning: Ignoring unknown parameters: bins
jaccard_perm_df %>%
ggplot(.) +
aes(Jaccard, color = Group) +
facet_grid(Group ~ .) +
geom_boxplot(bins = 50)
## Warning: Ignoring unknown parameters: bins
jaccard_perm_df %>%
ggplot(.) +
aes(x = Group, y = Jaccard) +
geom_violin()
These plots show that the mean differences in Jaccard indices are reflected in the participants’ data are shown in the permuted data, too. This makes sense since the participants detected regularities and sorted the exemplars into different numbers of sets. In permuting the exemplar identifiers within participants, we keep some of this structure.
Let’s try aggregating the by-exemplar statistics.
jaccard_perm_stats_df <- rbind(P1_perm_stats_df, P31M_perm_stats_df, P3M1_perm_stats_df, P6_perm_stats_df, P6M_perm_stats_df)
# Sort by group, exemplar_pair
jaccard_perm_stats_df <- jaccard_perm_stats_df %>%
dplyr::arrange(Group, exemplar_pair)
jaccard_perm_stats_df %>%
ggplot(.) +
aes(x = jaccard_mean, fill = Group) +
geom_histogram() +
facet_grid(Group ~ .) +
ggtitle("Mean exemplar-pair Jaccard indices for permuted data")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
jaccard_perm_stats_df %>%
ggplot(.) +
aes(x = jaccard_sd, fill = Group) +
geom_histogram() +
facet_grid(Group ~ .) +
ggtitle("Standard deviation of exemplar-pair Jaccard indices for permuted data")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Load the observed data and clean it.
jaccard_observed_df <-
readr::read_csv("analysis/data/jaccard-no-duplicates.csv")
##
## ── Column specification ────────────────────────────────────────────────────────
## cols(
## Exemplar.Row = col_double(),
## Exemplar.Col = col_double(),
## Jaccard = col_double(),
## Group = col_character()
## )
jaccard_observed_df <- jaccard_observed_df %>%
dplyr::mutate(.,
exemplar_pair = paste0(
stringr::str_extract(Exemplar.Row, "[0-9]{3}$"),
"-",
stringr::str_extract(Exemplar.Col, "[0-9]{3}$")
)) %>%
dplyr::arrange(., Group, exemplar_pair)
Now, merge the permuted data with the observed data.
jaccard_merged_df <- dplyr::left_join(jaccard_perm_stats_df,
jaccard_observed_df,
by = c("Group", "exemplar_pair"))
# Rearrange columns for convenience
jaccard_merged_df <- jaccard_merged_df %>%
dplyr::select(., Group, exemplar_pair, Jaccard, jaccard_mean, jaccard_sd, Exemplar.Row, Exemplar.Col)
# Rename variables for clarity
jaccard_merged_df <- jaccard_merged_df %>%
dplyr::rename(., group = Group, jaccard_obs = Jaccard,
jaccard_emp_mean = jaccard_mean,
jaccard_emp_sd = jaccard_sd,
exemplar_row = Exemplar.Row,
exemplar_col = Exemplar.Col)
Calculate empirical z as \(z_{emp}=J_{obs}-\mu_{J}\) for each exemplar pair.
jaccard_merged_df <- jaccard_merged_df %>%
dplyr::mutate(., z_emp = (jaccard_obs-jaccard_emp_mean)/jaccard_emp_sd,
p_z_emp = pnorm(z_emp, jaccard_emp_mean, jaccard_emp_sd, lower.tail = FALSE))
Plot a histogram of z_emp.
jaccard_merged_df %>%
ggplot(.) +
aes(z_emp, fill = group) +
geom_histogram() +
facet_grid(group ~ .)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Curiously, P31M, P6, P6M and P3M1 have exemplar pairs whose observed Jaccard indices are substantially larger than the empirically derived reference (null) distribution even though the mean Jaccard indices for P1 are the largest.
Just for fun, let’s print the exemplar pairs whose z_emp exceeds some criterion \(z\) values.
We’ll use a two-tailed criterion value.
p_crit <- .0001
z_crit <- qnorm(p = 1-.5*(p_crit))
j_emp_p0001 <- jaccard_merged_df %>%
dplyr::filter(., z_emp > z_crit) %>%
dplyr::arrange(., group, desc(jaccard_emp_mean))
knitr::kable(j_emp_p0001)
| group | exemplar_pair | jaccard_obs | jaccard_emp_mean | jaccard_emp_sd | exemplar_row | exemplar_col | z_emp | p_z_emp |
|---|---|---|---|---|---|---|---|---|
| P1 | 008-009 | 0.4347826 | 0.1997302 | 0.0523893 | 101008 | 101009 | 4.486650 | 0 |
| P31M | 006-016 | 0.3469388 | 0.1544913 | 0.0455907 | 115006 | 115016 | 4.221202 | 0 |
| P31M | 002-020 | 0.4347826 | 0.1541413 | 0.0445330 | 115002 | 115020 | 6.301875 | 0 |
| P31M | 004-009 | 0.4666667 | 0.1536301 | 0.0458028 | 115004 | 115009 | 6.834437 | 0 |
| P31M | 008-015 | 0.3469388 | 0.1534583 | 0.0454080 | 115008 | 115015 | 4.260934 | 0 |
| P31M | 014-020 | 0.5000000 | 0.1532609 | 0.0443117 | 115014 | 115020 | 7.824999 | 0 |
| P31M | 007-020 | 0.3469388 | 0.1530137 | 0.0472758 | 115007 | 115020 | 4.101998 | 0 |
| P31M | 002-007 | 0.6500000 | 0.1528091 | 0.0456546 | 115002 | 115007 | 10.890260 | 0 |
| P31M | 002-014 | 0.4347826 | 0.1523665 | 0.0464296 | 115002 | 115014 | 6.082672 | 0 |
| P31M | 007-014 | 0.3469388 | 0.1520057 | 0.0465605 | 115007 | 115014 | 4.186665 | 0 |
| P31M | 009-014 | 0.3469388 | 0.1501004 | 0.0442869 | 115009 | 115014 | 4.444622 | 0 |
| P3M1 | 019-020 | 0.4042553 | 0.1436215 | 0.0475534 | 114019 | 114020 | 5.480869 | 0 |
| P3M1 | 003-016 | 0.3469388 | 0.1431156 | 0.0447568 | 114003 | 114016 | 4.554010 | 0 |
| P3M1 | 011-019 | 0.3750000 | 0.1415372 | 0.0445837 | 114011 | 114019 | 5.236508 | 0 |
| P6 | 001-017 | 0.3200000 | 0.1384481 | 0.0436607 | 116001 | 116017 | 4.158245 | 0 |
| P6 | 007-009 | 0.4666667 | 0.1380211 | 0.0441697 | 116007 | 116009 | 7.440517 | 0 |
| P6 | 014-017 | 0.3200000 | 0.1376545 | 0.0451294 | 116014 | 116017 | 4.040509 | 0 |
| P6 | 013-019 | 0.4888889 | 0.1373315 | 0.0433875 | 116013 | 116019 | 8.102725 | 0 |
| P6 | 005-013 | 0.3333333 | 0.1365565 | 0.0442138 | 116005 | 116013 | 4.450579 | 0 |
| P6 | 002-011 | 0.4042553 | 0.1363300 | 0.0431172 | 116002 | 116011 | 6.213881 | 0 |
| P6 | 008-009 | 0.3541667 | 0.1361674 | 0.0434391 | 116008 | 116009 | 5.018501 | 0 |
| P6 | 008-020 | 0.3265306 | 0.1359853 | 0.0425070 | 116008 | 116020 | 4.482680 | 0 |
| P6 | 006-019 | 0.4666667 | 0.1356848 | 0.0441123 | 116006 | 116019 | 7.503171 | 0 |
| P6 | 003-014 | 0.3265306 | 0.1354559 | 0.0438507 | 116003 | 116014 | 4.357394 | 0 |
| P6 | 006-013 | 0.5581395 | 0.1348380 | 0.0450430 | 116006 | 116013 | 9.397711 | 0 |
| P6M | 008-010 | 0.3333333 | 0.1448769 | 0.0455945 | 117008 | 117010 | 4.133318 | 0 |
| P6M | 008-020 | 0.3541667 | 0.1437420 | 0.0410528 | 117008 | 117020 | 5.125709 | 0 |
| P6M | 001-011 | 0.3333333 | 0.1433422 | 0.0465964 | 117001 | 117011 | 4.077378 | 0 |
| P6M | 010-020 | 0.3829787 | 0.1432528 | 0.0453747 | 117010 | 117020 | 5.283256 | 0 |
xtabs(~ group, j_emp_p0001)
## group
## P1 P31M P3M1 P6 P6M
## 1 10 3 11 4
p_crit <- .001
z_crit <- qnorm(p = 1-.5*(p_crit))
j_emp_p001 <- jaccard_merged_df %>%
dplyr::filter(., z_emp > z_crit) %>%
dplyr::arrange(., group, desc(jaccard_emp_mean))
knitr::kable(j_emp_p001)
| group | exemplar_pair | jaccard_obs | jaccard_emp_mean | jaccard_emp_sd | exemplar_row | exemplar_col | z_emp | p_z_emp |
|---|---|---|---|---|---|---|---|---|
| P1 | 016-020 | 0.3750000 | 0.2026614 | 0.0511486 | 101016 | 101020 | 3.369369 | 0 |
| P1 | 010-016 | 0.4042553 | 0.2019869 | 0.0520852 | 101010 | 101016 | 3.883416 | 0 |
| P1 | 007-019 | 0.3750000 | 0.2007621 | 0.0501171 | 101007 | 101019 | 3.476615 | 0 |
| P1 | 008-009 | 0.4347826 | 0.1997302 | 0.0523893 | 101008 | 101009 | 4.486650 | 0 |
| P31M | 006-016 | 0.3469388 | 0.1544913 | 0.0455907 | 115006 | 115016 | 4.221202 | 0 |
| P31M | 002-020 | 0.4347826 | 0.1541413 | 0.0445330 | 115002 | 115020 | 6.301875 | 0 |
| P31M | 004-009 | 0.4666667 | 0.1536301 | 0.0458028 | 115004 | 115009 | 6.834437 | 0 |
| P31M | 008-015 | 0.3469388 | 0.1534583 | 0.0454080 | 115008 | 115015 | 4.260934 | 0 |
| P31M | 014-020 | 0.5000000 | 0.1532609 | 0.0443117 | 115014 | 115020 | 7.824999 | 0 |
| P31M | 007-020 | 0.3469388 | 0.1530137 | 0.0472758 | 115007 | 115020 | 4.101998 | 0 |
| P31M | 002-007 | 0.6500000 | 0.1528091 | 0.0456546 | 115002 | 115007 | 10.890260 | 0 |
| P31M | 002-014 | 0.4347826 | 0.1523665 | 0.0464296 | 115002 | 115014 | 6.082672 | 0 |
| P31M | 006-019 | 0.3200000 | 0.1522070 | 0.0470140 | 115006 | 115019 | 3.569003 | 0 |
| P31M | 007-014 | 0.3469388 | 0.1520057 | 0.0465605 | 115007 | 115014 | 4.186665 | 0 |
| P31M | 009-014 | 0.3469388 | 0.1501004 | 0.0442869 | 115009 | 115014 | 4.444622 | 0 |
| P3M1 | 008-012 | 0.3200000 | 0.1467831 | 0.0481581 | 114008 | 114012 | 3.596836 | 0 |
| P3M1 | 019-020 | 0.4042553 | 0.1436215 | 0.0475534 | 114019 | 114020 | 5.480869 | 0 |
| P3M1 | 003-016 | 0.3469388 | 0.1431156 | 0.0447568 | 114003 | 114016 | 4.554010 | 0 |
| P3M1 | 008-014 | 0.2941176 | 0.1420000 | 0.0448338 | 114008 | 114014 | 3.392920 | 0 |
| P3M1 | 008-013 | 0.2941176 | 0.1418432 | 0.0454661 | 114008 | 114013 | 3.349187 | 0 |
| P3M1 | 011-019 | 0.3750000 | 0.1415372 | 0.0445837 | 114011 | 114019 | 5.236508 | 0 |
| P3M1 | 015-020 | 0.2941176 | 0.1410353 | 0.0429412 | 114015 | 114020 | 3.564931 | 0 |
| P3M1 | 003-010 | 0.2941176 | 0.1406768 | 0.0447781 | 114003 | 114010 | 3.426691 | 0 |
| P6 | 001-017 | 0.3200000 | 0.1384481 | 0.0436607 | 116001 | 116017 | 4.158245 | 0 |
| P6 | 007-009 | 0.4666667 | 0.1380211 | 0.0441697 | 116007 | 116009 | 7.440517 | 0 |
| P6 | 014-017 | 0.3200000 | 0.1376545 | 0.0451294 | 116014 | 116017 | 4.040509 | 0 |
| P6 | 013-019 | 0.4888889 | 0.1373315 | 0.0433875 | 116013 | 116019 | 8.102725 | 0 |
| P6 | 005-013 | 0.3333333 | 0.1365565 | 0.0442138 | 116005 | 116013 | 4.450579 | 0 |
| P6 | 002-011 | 0.4042553 | 0.1363300 | 0.0431172 | 116002 | 116011 | 6.213881 | 0 |
| P6 | 008-009 | 0.3541667 | 0.1361674 | 0.0434391 | 116008 | 116009 | 5.018501 | 0 |
| P6 | 008-020 | 0.3265306 | 0.1359853 | 0.0425070 | 116008 | 116020 | 4.482680 | 0 |
| P6 | 006-019 | 0.4666667 | 0.1356848 | 0.0441123 | 116006 | 116019 | 7.503171 | 0 |
| P6 | 012-016 | 0.2941176 | 0.1356635 | 0.0426123 | 116012 | 116016 | 3.718506 | 0 |
| P6 | 003-014 | 0.3265306 | 0.1354559 | 0.0438507 | 116003 | 116014 | 4.357394 | 0 |
| P6 | 006-013 | 0.5581395 | 0.1348380 | 0.0450430 | 116006 | 116013 | 9.397711 | 0 |
| P6M | 001-009 | 0.3265306 | 0.1465073 | 0.0478002 | 117001 | 117009 | 3.766165 | 0 |
| P6M | 010-013 | 0.3061224 | 0.1455597 | 0.0449610 | 117010 | 117013 | 3.571153 | 0 |
| P6M | 003-018 | 0.3125000 | 0.1455053 | 0.0459697 | 117003 | 117018 | 3.632710 | 0 |
| P6M | 008-010 | 0.3333333 | 0.1448769 | 0.0455945 | 117008 | 117010 | 4.133318 | 0 |
| P6M | 013-016 | 0.3061224 | 0.1444453 | 0.0459377 | 117013 | 117016 | 3.519484 | 0 |
| P6M | 002-005 | 0.3000000 | 0.1440870 | 0.0464512 | 117002 | 117005 | 3.356491 | 0 |
| P6M | 008-020 | 0.3541667 | 0.1437420 | 0.0410528 | 117008 | 117020 | 5.125709 | 0 |
| P6M | 001-011 | 0.3333333 | 0.1433422 | 0.0465964 | 117001 | 117011 | 4.077378 | 0 |
| P6M | 010-020 | 0.3829787 | 0.1432528 | 0.0453747 | 117010 | 117020 | 5.283256 | 0 |
| P6M | 015-018 | 0.3125000 | 0.1423195 | 0.0447096 | 117015 | 117018 | 3.806353 | 0 |
xtabs(~ group, j_emp_p001)
## group
## P1 P31M P3M1 P6 P6M
## 4 11 8 12 10
p_crit <- .01
z_crit <- qnorm(p = 1-.5*(p_crit))
j_emp_p01 <- jaccard_merged_df %>%
dplyr::filter(., z_emp > z_crit) %>%
dplyr::arrange(., group, desc(jaccard_emp_mean))
knitr::kable(j_emp_p01)
| group | exemplar_pair | jaccard_obs | jaccard_emp_mean | jaccard_emp_sd | exemplar_row | exemplar_col | z_emp | p_z_emp |
|---|---|---|---|---|---|---|---|---|
| P1 | 016-020 | 0.3750000 | 0.2026614 | 0.0511486 | 101016 | 101020 | 3.369369 | 0 |
| P1 | 010-015 | 0.3469388 | 0.2025179 | 0.0526086 | 101010 | 101015 | 2.745197 | 0 |
| P1 | 010-016 | 0.4042553 | 0.2019869 | 0.0520852 | 101010 | 101016 | 3.883416 | 0 |
| P1 | 007-019 | 0.3750000 | 0.2007621 | 0.0501171 | 101007 | 101019 | 3.476615 | 0 |
| P1 | 010-020 | 0.3469388 | 0.1999799 | 0.0512336 | 101010 | 101020 | 2.868407 | 0 |
| P1 | 008-009 | 0.4347826 | 0.1997302 | 0.0523893 | 101008 | 101009 | 4.486650 | 0 |
| P31M | 006-016 | 0.3469388 | 0.1544913 | 0.0455907 | 115006 | 115016 | 4.221202 | 0 |
| P31M | 002-020 | 0.4347826 | 0.1541413 | 0.0445330 | 115002 | 115020 | 6.301875 | 0 |
| P31M | 004-009 | 0.4666667 | 0.1536301 | 0.0458028 | 115004 | 115009 | 6.834437 | 0 |
| P31M | 008-015 | 0.3469388 | 0.1534583 | 0.0454080 | 115008 | 115015 | 4.260934 | 0 |
| P31M | 014-020 | 0.5000000 | 0.1532609 | 0.0443117 | 115014 | 115020 | 7.824999 | 0 |
| P31M | 004-014 | 0.2941176 | 0.1530242 | 0.0461496 | 115004 | 115014 | 3.057303 | 0 |
| P31M | 007-020 | 0.3469388 | 0.1530137 | 0.0472758 | 115007 | 115020 | 4.101998 | 0 |
| P31M | 015-019 | 0.2941176 | 0.1529676 | 0.0473107 | 115015 | 115019 | 2.983468 | 0 |
| P31M | 002-007 | 0.6500000 | 0.1528091 | 0.0456546 | 115002 | 115007 | 10.890260 | 0 |
| P31M | 002-014 | 0.4347826 | 0.1523665 | 0.0464296 | 115002 | 115014 | 6.082672 | 0 |
| P31M | 006-019 | 0.3200000 | 0.1522070 | 0.0470140 | 115006 | 115019 | 3.569003 | 0 |
| P31M | 011-016 | 0.2941176 | 0.1520355 | 0.0482082 | 115011 | 115016 | 2.947260 | 0 |
| P31M | 007-014 | 0.3469388 | 0.1520057 | 0.0465605 | 115007 | 115014 | 4.186665 | 0 |
| P31M | 013-018 | 0.2941176 | 0.1514879 | 0.0469310 | 115013 | 115018 | 3.039140 | 0 |
| P31M | 010-013 | 0.2941176 | 0.1511875 | 0.0466110 | 115010 | 115013 | 3.066448 | 0 |
| P31M | 011-015 | 0.2692308 | 0.1504190 | 0.0458878 | 115011 | 115015 | 2.589182 | 0 |
| P31M | 009-014 | 0.3469388 | 0.1501004 | 0.0442869 | 115009 | 115014 | 4.444622 | 0 |
| P3M1 | 008-012 | 0.3200000 | 0.1467831 | 0.0481581 | 114008 | 114012 | 3.596836 | 0 |
| P3M1 | 011-020 | 0.2692308 | 0.1437663 | 0.0464568 | 114011 | 114020 | 2.700667 | 0 |
| P3M1 | 019-020 | 0.4042553 | 0.1436215 | 0.0475534 | 114019 | 114020 | 5.480869 | 0 |
| P3M1 | 003-016 | 0.3469388 | 0.1431156 | 0.0447568 | 114003 | 114016 | 4.554010 | 0 |
| P3M1 | 008-014 | 0.2941176 | 0.1420000 | 0.0448338 | 114008 | 114014 | 3.392920 | 0 |
| P3M1 | 008-013 | 0.2941176 | 0.1418432 | 0.0454661 | 114008 | 114013 | 3.349187 | 0 |
| P3M1 | 003-017 | 0.2941176 | 0.1418300 | 0.0474815 | 114003 | 114017 | 3.207302 | 0 |
| P3M1 | 012-017 | 0.2692308 | 0.1417132 | 0.0456949 | 114012 | 114017 | 2.790632 | 0 |
| P3M1 | 011-019 | 0.3750000 | 0.1415372 | 0.0445837 | 114011 | 114019 | 5.236508 | 0 |
| P3M1 | 013-017 | 0.2692308 | 0.1412909 | 0.0445063 | 114013 | 114017 | 2.874649 | 0 |
| P3M1 | 015-020 | 0.2941176 | 0.1410353 | 0.0429412 | 114015 | 114020 | 3.564931 | 0 |
| P3M1 | 003-010 | 0.2941176 | 0.1406768 | 0.0447781 | 114003 | 114010 | 3.426691 | 0 |
| P6 | 001-017 | 0.3200000 | 0.1384481 | 0.0436607 | 116001 | 116017 | 4.158245 | 0 |
| P6 | 007-009 | 0.4666667 | 0.1380211 | 0.0441697 | 116007 | 116009 | 7.440517 | 0 |
| P6 | 001-018 | 0.2692308 | 0.1379620 | 0.0438256 | 116001 | 116018 | 2.995250 | 0 |
| P6 | 017-018 | 0.2692308 | 0.1378323 | 0.0450538 | 116017 | 116018 | 2.916482 | 0 |
| P6 | 014-017 | 0.3200000 | 0.1376545 | 0.0451294 | 116014 | 116017 | 4.040509 | 0 |
| P6 | 015-018 | 0.2500000 | 0.1374907 | 0.0435567 | 116015 | 116018 | 2.583053 | 0 |
| P6 | 013-019 | 0.4888889 | 0.1373315 | 0.0433875 | 116013 | 116019 | 8.102725 | 0 |
| P6 | 007-008 | 0.2500000 | 0.1369494 | 0.0434299 | 116007 | 116008 | 2.603059 | 0 |
| P6 | 005-013 | 0.3333333 | 0.1365565 | 0.0442138 | 116005 | 116013 | 4.450579 | 0 |
| P6 | 002-011 | 0.4042553 | 0.1363300 | 0.0431172 | 116002 | 116011 | 6.213881 | 0 |
| P6 | 008-009 | 0.3541667 | 0.1361674 | 0.0434391 | 116008 | 116009 | 5.018501 | 0 |
| P6 | 008-020 | 0.3265306 | 0.1359853 | 0.0425070 | 116008 | 116020 | 4.482680 | 0 |
| P6 | 006-019 | 0.4666667 | 0.1356848 | 0.0441123 | 116006 | 116019 | 7.503171 | 0 |
| P6 | 012-016 | 0.2941176 | 0.1356635 | 0.0426123 | 116012 | 116016 | 3.718506 | 0 |
| P6 | 004-010 | 0.2692308 | 0.1356585 | 0.0453429 | 116004 | 116010 | 2.945823 | 0 |
| P6 | 003-014 | 0.3265306 | 0.1354559 | 0.0438507 | 116003 | 116014 | 4.357394 | 0 |
| P6 | 006-013 | 0.5581395 | 0.1348380 | 0.0450430 | 116006 | 116013 | 9.397711 | 0 |
| P6M | 006-017 | 0.2857143 | 0.1469697 | 0.0447717 | 117006 | 117017 | 3.098934 | 0 |
| P6M | 001-009 | 0.3265306 | 0.1465073 | 0.0478002 | 117001 | 117009 | 3.766165 | 0 |
| P6M | 010-013 | 0.3061224 | 0.1455597 | 0.0449610 | 117010 | 117013 | 3.571153 | 0 |
| P6M | 003-018 | 0.3125000 | 0.1455053 | 0.0459697 | 117003 | 117018 | 3.632710 | 0 |
| P6M | 008-010 | 0.3333333 | 0.1448769 | 0.0455945 | 117008 | 117010 | 4.133318 | 0 |
| P6M | 013-016 | 0.3061224 | 0.1444453 | 0.0459377 | 117013 | 117016 | 3.519484 | 0 |
| P6M | 001-013 | 0.2800000 | 0.1441186 | 0.0475129 | 117001 | 117013 | 2.859881 | 0 |
| P6M | 002-005 | 0.3000000 | 0.1440870 | 0.0464512 | 117002 | 117005 | 3.356491 | 0 |
| P6M | 008-020 | 0.3541667 | 0.1437420 | 0.0410528 | 117008 | 117020 | 5.125709 | 0 |
| P6M | 010-019 | 0.2800000 | 0.1437261 | 0.0444244 | 117010 | 117019 | 3.067549 | 0 |
| P6M | 013-020 | 0.2745098 | 0.1435044 | 0.0457516 | 117013 | 117020 | 2.863408 | 0 |
| P6M | 001-011 | 0.3333333 | 0.1433422 | 0.0465964 | 117001 | 117011 | 4.077378 | 0 |
| P6M | 010-020 | 0.3829787 | 0.1432528 | 0.0453747 | 117010 | 117020 | 5.283256 | 0 |
| P6M | 008-013 | 0.2800000 | 0.1431326 | 0.0453443 | 117008 | 117013 | 3.018404 | 0 |
| P6M | 015-018 | 0.3125000 | 0.1423195 | 0.0447096 | 117015 | 117018 | 3.806353 | 0 |
xtabs(~ group, j_emp_p01)
## group
## P1 P31M P3M1 P6 P6M
## 6 17 12 17 15
p_crit <- .05
z_crit <- qnorm(p = 1-.5*(p_crit))
j_emp_p05 <- jaccard_merged_df %>%
dplyr::filter(., z_emp > z_crit) %>%
dplyr::arrange(., group, desc(jaccard_emp_mean))
knitr::kable(j_emp_p05)
| group | exemplar_pair | jaccard_obs | jaccard_emp_mean | jaccard_emp_sd | exemplar_row | exemplar_col | z_emp | p_z_emp |
|---|---|---|---|---|---|---|---|---|
| P1 | 016-020 | 0.3750000 | 0.2026614 | 0.0511486 | 101016 | 101020 | 3.369369 | 0 |
| P1 | 010-015 | 0.3469388 | 0.2025179 | 0.0526086 | 101010 | 101015 | 2.745197 | 0 |
| P1 | 002-011 | 0.3265306 | 0.2022794 | 0.0509974 | 101002 | 101011 | 2.436422 | 0 |
| P1 | 004-006 | 0.3200000 | 0.2020502 | 0.0520419 | 101004 | 101006 | 2.266437 | 0 |
| P1 | 016-017 | 0.3200000 | 0.2019904 | 0.0517065 | 101016 | 101017 | 2.282295 | 0 |
| P1 | 010-016 | 0.4042553 | 0.2019869 | 0.0520852 | 101010 | 101016 | 3.883416 | 0 |
| P1 | 019-020 | 0.3200000 | 0.2019041 | 0.0514376 | 101019 | 101020 | 2.295904 | 0 |
| P1 | 003-015 | 0.3200000 | 0.2016781 | 0.0544723 | 101003 | 101015 | 2.172147 | 0 |
| P1 | 001-015 | 0.3200000 | 0.2015624 | 0.0525580 | 101001 | 101015 | 2.253462 | 0 |
| P1 | 007-012 | 0.3200000 | 0.2014882 | 0.0542545 | 101007 | 101012 | 2.184367 | 0 |
| P1 | 007-015 | 0.3200000 | 0.2012488 | 0.0520508 | 101007 | 101015 | 2.281448 | 0 |
| P1 | 007-019 | 0.3750000 | 0.2007621 | 0.0501171 | 101007 | 101019 | 3.476615 | 0 |
| P1 | 010-020 | 0.3469388 | 0.1999799 | 0.0512336 | 101010 | 101020 | 2.868407 | 0 |
| P1 | 008-009 | 0.4347826 | 0.1997302 | 0.0523893 | 101008 | 101009 | 4.486650 | 0 |
| P31M | 006-016 | 0.3469388 | 0.1544913 | 0.0455907 | 115006 | 115016 | 4.221202 | 0 |
| P31M | 009-020 | 0.2692308 | 0.1543772 | 0.0455129 | 115009 | 115020 | 2.523536 | 0 |
| P31M | 002-020 | 0.4347826 | 0.1541413 | 0.0445330 | 115002 | 115020 | 6.301875 | 0 |
| P31M | 016-017 | 0.2692308 | 0.1539553 | 0.0456523 | 115016 | 115017 | 2.525074 | 0 |
| P31M | 010-015 | 0.2452830 | 0.1537649 | 0.0460724 | 115010 | 115015 | 1.986398 | 0 |
| P31M | 004-009 | 0.4666667 | 0.1536301 | 0.0458028 | 115004 | 115009 | 6.834437 | 0 |
| P31M | 006-015 | 0.2692308 | 0.1535847 | 0.0466486 | 115006 | 115015 | 2.479090 | 0 |
| P31M | 008-015 | 0.3469388 | 0.1534583 | 0.0454080 | 115008 | 115015 | 4.260934 | 0 |
| P31M | 014-020 | 0.5000000 | 0.1532609 | 0.0443117 | 115014 | 115020 | 7.824999 | 0 |
| P31M | 004-014 | 0.2941176 | 0.1530242 | 0.0461496 | 115004 | 115014 | 3.057303 | 0 |
| P31M | 007-020 | 0.3469388 | 0.1530137 | 0.0472758 | 115007 | 115020 | 4.101998 | 0 |
| P31M | 015-019 | 0.2941176 | 0.1529676 | 0.0473107 | 115015 | 115019 | 2.983468 | 0 |
| P31M | 002-007 | 0.6500000 | 0.1528091 | 0.0456546 | 115002 | 115007 | 10.890260 | 0 |
| P31M | 004-020 | 0.2452830 | 0.1527105 | 0.0458227 | 115004 | 115020 | 2.020234 | 0 |
| P31M | 008-019 | 0.2692308 | 0.1524873 | 0.0456175 | 115008 | 115019 | 2.559180 | 0 |
| P31M | 003-005 | 0.2452830 | 0.1524094 | 0.0458820 | 115003 | 115005 | 2.024186 | 0 |
| P31M | 001-008 | 0.2452830 | 0.1523676 | 0.0459000 | 115001 | 115008 | 2.024300 | 0 |
| P31M | 002-014 | 0.4347826 | 0.1523665 | 0.0464296 | 115002 | 115014 | 6.082672 | 0 |
| P31M | 003-010 | 0.2452830 | 0.1523455 | 0.0468872 | 115003 | 115010 | 1.982150 | 0 |
| P31M | 010-016 | 0.2692308 | 0.1522625 | 0.0462861 | 115010 | 115016 | 2.527071 | 0 |
| P31M | 006-019 | 0.3200000 | 0.1522070 | 0.0470140 | 115006 | 115019 | 3.569003 | 0 |
| P31M | 008-012 | 0.2452830 | 0.1520735 | 0.0468120 | 115008 | 115012 | 1.991144 | 0 |
| P31M | 013-016 | 0.2692308 | 0.1520686 | 0.0464882 | 115013 | 115016 | 2.520255 | 0 |
| P31M | 011-016 | 0.2941176 | 0.1520355 | 0.0482082 | 115011 | 115016 | 2.947260 | 0 |
| P31M | 006-011 | 0.2452830 | 0.1520303 | 0.0471372 | 115006 | 115011 | 1.978325 | 0 |
| P31M | 007-014 | 0.3469388 | 0.1520057 | 0.0465605 | 115007 | 115014 | 4.186665 | 0 |
| P31M | 005-018 | 0.2452830 | 0.1514984 | 0.0465938 | 115005 | 115018 | 2.012812 | 0 |
| P31M | 013-018 | 0.2941176 | 0.1514879 | 0.0469310 | 115013 | 115018 | 3.039140 | 0 |
| P31M | 010-013 | 0.2941176 | 0.1511875 | 0.0466110 | 115010 | 115013 | 3.066448 | 0 |
| P31M | 002-009 | 0.2452830 | 0.1511269 | 0.0451101 | 115002 | 115009 | 2.087248 | 0 |
| P31M | 013-019 | 0.2692308 | 0.1508800 | 0.0464156 | 115013 | 115019 | 2.549807 | 0 |
| P31M | 010-011 | 0.2452830 | 0.1506905 | 0.0468336 | 115010 | 115011 | 2.019757 | 0 |
| P31M | 011-015 | 0.2692308 | 0.1504190 | 0.0458878 | 115011 | 115015 | 2.589182 | 0 |
| P31M | 009-014 | 0.3469388 | 0.1501004 | 0.0442869 | 115009 | 115014 | 4.444622 | 0 |
| P3M1 | 008-012 | 0.3200000 | 0.1467831 | 0.0481581 | 114008 | 114012 | 3.596836 | 0 |
| P3M1 | 003-018 | 0.2452830 | 0.1447031 | 0.0463087 | 114003 | 114018 | 2.171942 | 0 |
| P3M1 | 006-009 | 0.2452830 | 0.1444126 | 0.0423229 | 114006 | 114009 | 2.383354 | 0 |
| P3M1 | 004-019 | 0.2452830 | 0.1438403 | 0.0464733 | 114004 | 114019 | 2.182815 | 0 |
| P3M1 | 011-020 | 0.2692308 | 0.1437663 | 0.0464568 | 114011 | 114020 | 2.700667 | 0 |
| P3M1 | 019-020 | 0.4042553 | 0.1436215 | 0.0475534 | 114019 | 114020 | 5.480869 | 0 |
| P3M1 | 003-016 | 0.3469388 | 0.1431156 | 0.0447568 | 114003 | 114016 | 4.554010 | 0 |
| P3M1 | 016-018 | 0.2452830 | 0.1428453 | 0.0441724 | 114016 | 114018 | 2.319040 | 0 |
| P3M1 | 005-007 | 0.2452830 | 0.1426746 | 0.0441964 | 114005 | 114007 | 2.321646 | 0 |
| P3M1 | 008-014 | 0.2941176 | 0.1420000 | 0.0448338 | 114008 | 114014 | 3.392920 | 0 |
| P3M1 | 008-013 | 0.2941176 | 0.1418432 | 0.0454661 | 114008 | 114013 | 3.349187 | 0 |
| P3M1 | 003-017 | 0.2941176 | 0.1418300 | 0.0474815 | 114003 | 114017 | 3.207302 | 0 |
| P3M1 | 002-012 | 0.2452830 | 0.1417180 | 0.0458268 | 114002 | 114012 | 2.259921 | 0 |
| P3M1 | 012-017 | 0.2692308 | 0.1417132 | 0.0456949 | 114012 | 114017 | 2.790632 | 0 |
| P3M1 | 007-015 | 0.2452830 | 0.1416145 | 0.0453829 | 114007 | 114015 | 2.284309 | 0 |
| P3M1 | 011-019 | 0.3750000 | 0.1415372 | 0.0445837 | 114011 | 114019 | 5.236508 | 0 |
| P3M1 | 013-017 | 0.2692308 | 0.1412909 | 0.0445063 | 114013 | 114017 | 2.874649 | 0 |
| P3M1 | 015-020 | 0.2941176 | 0.1410353 | 0.0429412 | 114015 | 114020 | 3.564931 | 0 |
| P3M1 | 004-011 | 0.2452830 | 0.1409725 | 0.0456179 | 114004 | 114011 | 2.286614 | 0 |
| P3M1 | 003-010 | 0.2941176 | 0.1406768 | 0.0447781 | 114003 | 114010 | 3.426691 | 0 |
| P3M1 | 010-011 | 0.2452830 | 0.1404196 | 0.0459566 | 114010 | 114011 | 2.281792 | 0 |
| P6 | 001-017 | 0.3200000 | 0.1384481 | 0.0436607 | 116001 | 116017 | 4.158245 | 0 |
| P6 | 007-009 | 0.4666667 | 0.1380211 | 0.0441697 | 116007 | 116009 | 7.440517 | 0 |
| P6 | 001-018 | 0.2692308 | 0.1379620 | 0.0438256 | 116001 | 116018 | 2.995250 | 0 |
| P6 | 017-018 | 0.2692308 | 0.1378323 | 0.0450538 | 116017 | 116018 | 2.916482 | 0 |
| P6 | 014-017 | 0.3200000 | 0.1376545 | 0.0451294 | 116014 | 116017 | 4.040509 | 0 |
| P6 | 005-007 | 0.2407407 | 0.1375631 | 0.0450893 | 116005 | 116007 | 2.288294 | 0 |
| P6 | 015-018 | 0.2500000 | 0.1374907 | 0.0435567 | 116015 | 116018 | 2.583053 | 0 |
| P6 | 013-019 | 0.4888889 | 0.1373315 | 0.0433875 | 116013 | 116019 | 8.102725 | 0 |
| P6 | 005-019 | 0.2407407 | 0.1370936 | 0.0432307 | 116005 | 116019 | 2.397533 | 0 |
| P6 | 014-018 | 0.2452830 | 0.1370532 | 0.0432897 | 116014 | 116018 | 2.500131 | 0 |
| P6 | 010-012 | 0.2222222 | 0.1369815 | 0.0428191 | 116010 | 116012 | 1.990716 | 0 |
| P6 | 004-020 | 0.2452830 | 0.1369799 | 0.0452552 | 116004 | 116020 | 2.393162 | 0 |
| P6 | 007-008 | 0.2500000 | 0.1369494 | 0.0434299 | 116007 | 116008 | 2.603059 | 0 |
| P6 | 005-013 | 0.3333333 | 0.1365565 | 0.0442138 | 116005 | 116013 | 4.450579 | 0 |
| P6 | 002-011 | 0.4042553 | 0.1363300 | 0.0431172 | 116002 | 116011 | 6.213881 | 0 |
| P6 | 017-019 | 0.2452830 | 0.1362403 | 0.0439990 | 116017 | 116019 | 2.478302 | 0 |
| P6 | 008-009 | 0.3541667 | 0.1361674 | 0.0434391 | 116008 | 116009 | 5.018501 | 0 |
| P6 | 008-020 | 0.3265306 | 0.1359853 | 0.0425070 | 116008 | 116020 | 4.482680 | 0 |
| P6 | 006-019 | 0.4666667 | 0.1356848 | 0.0441123 | 116006 | 116019 | 7.503171 | 0 |
| P6 | 012-016 | 0.2941176 | 0.1356635 | 0.0426123 | 116012 | 116016 | 3.718506 | 0 |
| P6 | 004-010 | 0.2692308 | 0.1356585 | 0.0453429 | 116004 | 116010 | 2.945823 | 0 |
| P6 | 004-012 | 0.2452830 | 0.1355501 | 0.0440347 | 116004 | 116012 | 2.491967 | 0 |
| P6 | 003-014 | 0.3265306 | 0.1354559 | 0.0438507 | 116003 | 116014 | 4.357394 | 0 |
| P6 | 006-013 | 0.5581395 | 0.1348380 | 0.0450430 | 116006 | 116013 | 9.397711 | 0 |
| P6M | 006-017 | 0.2857143 | 0.1469697 | 0.0447717 | 117006 | 117017 | 3.098934 | 0 |
| P6M | 001-009 | 0.3265306 | 0.1465073 | 0.0478002 | 117001 | 117009 | 3.766165 | 0 |
| P6M | 005-019 | 0.2500000 | 0.1459680 | 0.0447321 | 117005 | 117019 | 2.325667 | 0 |
| P6M | 008-009 | 0.2500000 | 0.1458103 | 0.0472835 | 117008 | 117009 | 2.203510 | 0 |
| P6M | 010-013 | 0.3061224 | 0.1455597 | 0.0449610 | 117010 | 117013 | 3.571153 | 0 |
| P6M | 003-018 | 0.3125000 | 0.1455053 | 0.0459697 | 117003 | 117018 | 3.632710 | 0 |
| P6M | 015-019 | 0.2549020 | 0.1452188 | 0.0454548 | 117015 | 117019 | 2.413016 | 0 |
| P6M | 014-017 | 0.2549020 | 0.1450481 | 0.0474809 | 117014 | 117017 | 2.313644 | 0 |
| P6M | 009-019 | 0.2500000 | 0.1449205 | 0.0471529 | 117009 | 117019 | 2.228485 | 0 |
| P6M | 008-010 | 0.3333333 | 0.1448769 | 0.0455945 | 117008 | 117010 | 4.133318 | 0 |
| P6M | 013-016 | 0.3061224 | 0.1444453 | 0.0459377 | 117013 | 117016 | 3.519484 | 0 |
| P6M | 005-017 | 0.2500000 | 0.1443246 | 0.0469896 | 117005 | 117017 | 2.248911 | 0 |
| P6M | 001-013 | 0.2800000 | 0.1441186 | 0.0475129 | 117001 | 117013 | 2.859881 | 0 |
| P6M | 002-005 | 0.3000000 | 0.1440870 | 0.0464512 | 117002 | 117005 | 3.356491 | 0 |
| P6M | 008-020 | 0.3541667 | 0.1437420 | 0.0410528 | 117008 | 117020 | 5.125709 | 0 |
| P6M | 010-019 | 0.2800000 | 0.1437261 | 0.0444244 | 117010 | 117019 | 3.067549 | 0 |
| P6M | 013-020 | 0.2745098 | 0.1435044 | 0.0457516 | 117013 | 117020 | 2.863408 | 0 |
| P6M | 001-011 | 0.3333333 | 0.1433422 | 0.0465964 | 117001 | 117011 | 4.077378 | 0 |
| P6M | 010-020 | 0.3829787 | 0.1432528 | 0.0453747 | 117010 | 117020 | 5.283256 | 0 |
| P6M | 008-013 | 0.2800000 | 0.1431326 | 0.0453443 | 117008 | 117013 | 3.018404 | 0 |
| P6M | 015-018 | 0.3125000 | 0.1423195 | 0.0447096 | 117015 | 117018 | 3.806353 | 0 |
xtabs(~ group, j_emp_p05)
## group
## P1 P31M P3M1 P6 P6M
## 14 34 21 24 21
jaccard_merged_df %>%
ggplot(.) +
aes(x = z_emp, fill = group) +
geom_histogram(bins = 20) +
geom_vline(xintercept = qnorm(1-.5*(.0001)), color = "black") +
geom_vline(xintercept = qnorm(1-.5*(.01)), color = "gray50") +
facet_grid(group ~ .)